An Improved Coupled Dynamic Modelling for Exploring Gearbox Vibrations Considering Local Defects

Gearbox is a key part in machinery,in which gear,shaft and bearing operate together to transmit motion and power.The wide usage and high failure rate of gearbox make it attract much attention on its health monitoring and fault diagnosis.Dynamic modelling can study the mechanism under different faults and provide theoretical foundation for fault detection.However,current commonly used gear dynamic model usually neglects the influence of bearing and shaft,resulting in incomplete understanding of gearbox fault diagnosis especially under the effect of local defects on gear and shaft.To address this problem,an improved gear-shaft-bearing-housing dynamic model is proposed to reveal the vibration mechanism and responses considering shaft whirling and gear local defects.Firstly,an eighteen degree-of-freedom gearbox dynamic model is proposed,taking into account the interaction among gear,bearing and shaft.Secondly,the dynamic model is iteratively solved.Then,vibration responses are expounded and analysed considering gear spalling and shaft crack.Numerical results show that the gear mesh frequency and its harmonics have higher amplitude through the spectrum.Vibration RMS and the shaft rotating frequency increase with the spalling size and shaft crack angle in general.An experiment is designed to verify the rationality of the proposed gearbox model.Lastly,comprehensive analysis under different spalling size and shaft crack angle are analysed.Results show that when spalling size and crack angle are larger,RMS and the amplitude of shaft rotating frequency will not increase linearly.The dynamic model can accurately simulate the vibration of gear transmission system,which is helpful for gearbox fault diagnosis.

Dynamic propagation problems concerning surfaces of asymmetrical mode III crack subjected to moving loads

With the theory of complex functions, dynamic propagation problems concerning surfaces of asymmetrical mode Ⅲ crack subjected to moving loads are investigated. General representations of analytical solutions are obtained with self-similar functions. The problems can be easily converted into Riemann-Hilbert problems using this technique. Analytical solutions to stress, displacement and dynamic stress intensity factor under constant and unit-step moving loads on the surfaces of asymmetrical extension crack, respectively, are obtained. By applying these solutions, together with the superposition principle, solutions of discretionarily intricate problems can be found.

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.

基于ABAQUS平台考虑T应力的Ⅰ型裂纹扩展模拟开发

工程结构在制造工艺过程中或使用期间会产生裂纹,对结构断裂路径的预测和研究是防治工程安全问题发生的重要手段。在考虑裂纹尖端应力场常数项T应力的基础上对传统的最大周向应力准则(Maximum tangential stress criterion,MTS)和最小应变能密度因子准则(Minimum strain energy density criterion,SED)进行修正,采用Python语言对ABAQUS的前、后处理和有限元计算模块进行二次开发,通过计算最优解的粒子群算法(Particle swarm optimization,PSO)将修正后的准则编入裂纹自动扩展程序脚本中。利用上述二次开发程序对初始纯Ⅰ型裂纹的扩展路径进行模拟,结果表明:采用ABAQUS脚本程序模拟结果与相关文献实验结果吻合,表明了程序的有效性,进而实现考虑T应力的多种断裂准则对裂纹扩展路径的预测;当T应力值处于一定范围内时,修正的MTS准则无法预测裂纹发生的偏转现象,扩展路径呈直线,此时可采用修正的SED准则进行预测。

Simultaneously measuring initiation toughness of pure mode Ⅰ and mode Ⅱ cracks subjected to impact loads

In order to simultaneously measure the initiation toughness of pure mode Ⅰ and mode Ⅱ cracks in one specimen,a large-size double-cracked concave-convex plate(DCCP)specimen configuration was proposed.Impacting tests were implemented in the drop plate impact device.Strain gauges were employed to measure impact loads and crack initiation time.The corresponding numerical model was established by using the dynamic finite difference program AUTODYN,and the experimental-numerical method and ABAQUS code were utilized to obtain the initial fracture toughness of the crack.Using experiments and numerical research,we concluded that the DCCP specimen is suitable for measuring the initial fracture toughness of pure mode Ⅰ and mode Ⅱ cracks at the same time;the dynamic initiation toughness increases with the increase of loading rate and the crack initiation time decreases with increasing loading rate;the initiation toughness of mode Ⅱ crack is 0.5 times that of mode Ⅰ crack when subjected to the same loading rate.For the pre-crack in the vicinity of the bottom of a sample,when its length increases from 20 to 100 mm,the dynamic initiation toughness of the pure mode Ⅰ crack gradually decreases,and the longer the lower crack length is,the easier the crack would initiate,but the dynamic initiation toughness of pure mode Ⅱ crack varies little.

(Ⅰ+Ⅱ)MIXED MODE HYDROGEN INDUCED CRACKING

Hydrogen induced cracking(HIC)of 0.3% C,1% Cr,1% Mn,1% Si high strength steel has been studied under simple mode Ⅰ,mode Ⅱ and(Ⅰ+Ⅱ)mixed mode loading conditions.Af- ter being hydrogen-charged in IN H_2SO_4 solution,the material behaved hydrogen embrittlement in all the cases studied.The threshold K_(ⅡH)/K_(ⅡX) of HIC under mode Ⅱ load- ing was 0.27,which was nearly the same as that K(ⅠH)/K_(ⅠX)=0.29 under mode Ⅰ loading. While the thresholds of-HIC under(Ⅰ+Ⅱ)mixed mode loading were 0.36,0.41 and 0.37 cor- responding to the K_Ⅱ/K_Ⅰ ratio of 0.27,0.4 and O.81.The results show that simple mode Ⅰ or mode Ⅱ loading is more susceptible to hydrogen embrittlement than(Ⅰ+Ⅱ)mixed mode. For explaining the experimental results,the effects of triaxial stress as well as plastic deformation ahead of crack tip has been discussed.

AN INVESTIGATION ON ASYMPTOTIC NEAR-TIP FIELDS OF DYNAMIC CRACK IN AN ELASTIC-PERFECTLY PLASTIC COMPRESSIBLE MATERIAL

The stress and deformation fields near the tip of a mode-I dynamic crack steadily propagating in an elastic-perfectly plastic compressible material are considered under plane strain conditions. Within the framework of infinitesimal displacement gradient theory, the material is characterized by the Von Mises yield criterion and the associated J(2) flow theory of plasticity. Through rigorous mathematical analysis, this paper eliminates the possibilities of elastic unloading and continuous asymptotic fields with singular deformation, and then constructs a fully continuous and bounded asymptotic stress and strain field. It is found that in this solution there exists a parameter phi(0) which cannot be determined by asymptotic analysis but may characterize the effect of the far field. Lastly the variations of continuous stresses, velocities and strains around the crack tip are given numerically for different values of phi(0).

A HALF PLANE CRACK UNDER THREE-DIMENSIONAL COMBINED MODE IMPACT LOADING

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is consid- ered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented.

Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.

Dislocation distribution model of mode Ⅲ propagation crack

Dislocation distribution functions of the edges of mode Ⅲ propagation crack subjected to three types of loads were studied by the methods of the theory of complex variable functions,by which,the problems researched were facilely transformed into Riemann-Hilbert problems and Keldysh-Sedov mixed boundary value problems. Analytical solutions of stresses,displacement and dynamic stress intensity factor were obtained by the measures of the theory of self-similar functions and corresponding differential and integral operation. In terms of the relationship between dislocation distribution functions and displacements,analytical solutions of dislocation distribution functions were obttained,and variational rules of dislocation distribution functions were depicted.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

ROUGHNESS-INDUCED SHEAR RESISTANCE OF MODE Ⅱ CRACK GROWTH

It is obtained in this paper that the fatigue threshold value of mode H was 1.9 times of that of mode Ⅰ in dual-phase steel(DPS),and the normal stress intensity factor range oJ mode Ⅱ branch crack tip was 2.2 times of that of mode Ⅰ.Above results illustrate that the resistance of mode Ⅱ crack growth was higher than that of mode Ⅰ,the former resulting from roughness-induced shear resistance,the latter,crack closure. The mode Ⅱ component can play two important roles in near-threshold fatigue crack growth:(1)increasing crack tip plasticity which accelerates the crack growth and(2)intro- ducing crack surface contact and rubbing to reduce the crack propagation rate.By means of crack closure,the quantity of shear resistance was easily solved in this paper.The friction shear stress strength factor range of mode Ⅱ,K_,is still much higher than the closure stress strength factor range of mode Ⅰ,K_(Ⅰ,cl).This illustrated that the roughness enlarged the second role and played a role of shielding crack tip from mode Ⅱ crack.

加载速率对高强钢40Cr和30CrMnSiNi2AⅠ型动态断裂韧性的影响

采用实验-数值方法对40Cr和30CrMnSiNi2A两种高强钢三点弯曲试样在不同加载速率的冲击载荷作用下进行了动态断裂韧性的测试,并对其率相关性进行研究．实验在Hopkinson压杆系统上完成,试样的起裂时间采用应变片法测得．结合有限元三维动态模拟,得到了不同加载速率下试样动态应力强度因子的时间历程并由实测的起裂时间确定材料动态断裂韧性．结果表明,在本工作加载速率范围内(10~6MPa·m^(1/2)/s),40Cr钢为解理型断裂,其动态断裂韧性随加载速率增加的变化趋势不明显；而30CrMnSiNi2A钢则在较大程度上表现为延性断裂的特征,其动态断裂韧性随加载速率的增加呈明显上升趋势．并对上述结果进行了宏观和微观机理分析．

国产HTPB复合固体推进剂Ⅰ-Ⅱ型裂纹断裂性能实验研究

采用WDN-10KN材料实验机对含Ⅰ-Ⅱ复合型裂纹的HTPB复合固体推进剂进行了拉伸速率为2mm.min-1的单轴拉伸试验,用摄像机记录了推进剂裂纹扩展至断裂的整个过程。得到了六种不同裂纹倾斜角下的力-变形曲线及裂纹扩展开裂角和断裂载荷。与T断裂准则、S断裂准则和σθ断裂准则进行比较,结果表明推进剂裂纹扩展开裂角与T断裂准则的数值计算结果较为接近,说明可以借助于T断裂准则对推进剂裂纹扩展的初始开裂角进行初步的理论预测。

混凝土Ⅰ-Ⅱ复合型裂缝扩展准则及扩展全过程的数值模拟

本文基于从试验中得出的混凝土Ⅰ-Ⅱ复合型裂缝起裂时的临界KⅠ-KⅡ曲线,提出了Ⅰ-Ⅱ复合型裂缝的扩展准则,即由外荷载在裂缝尖端产生的应力强度因子与虚拟裂缝黏聚力产生的应力强度因子的差大于或等于起裂时的临界KⅠ-KⅡ曲线时裂缝扩展,在此基础上采用有限元法对混凝土Ⅰ-Ⅱ复合型裂缝的起裂、稳定扩展及失稳扩展全过程进行了数值模拟,并计算了试件高度分别为2003、00、400、5006、00mm混凝土四点剪切梁的裂缝扩展路径、荷载-剪切位移曲线,数值模拟结果与试验结果吻合良好。研究表明,只要从试验中测得混凝土材料的Ⅰ-Ⅱ复合型裂缝起裂时的临界KⅠ-KⅡ曲线、抗拉强度及弹性模量,即可计算混凝土Ⅰ-Ⅱ复合型裂缝扩展全过程。

类岩石脆性材料非闭合裂纹的Ⅰ–Ⅱ压剪复合型断裂准则研究

实际工程中,结构体裂纹常处于拉剪和压剪复合受力状态,研究适合于复合型裂纹的断裂准则和裂纹扩展机理具有重要的理论意义和实用价值。以Ⅰ-Ⅱ复合型裂纹为研究对象,基于线弹性理论,在考虑裂纹几何特征及受力形式的基础上,系统介绍了裂纹应力强度因子(SIF)的理论解。提出了适用于Ⅱ型断裂的径向剪应力准则和双剪应力准则。对于Ⅰ-Ⅱ复合型裂纹,提出用等效Ⅰ、Ⅱ型SIF比值与Ⅰ、Ⅱ型断裂韧度比值的关系判定裂纹断裂类型,并分别选择适合于Ⅰ、Ⅱ型断裂的断裂准则,计算了裂纹断裂扩展理论角度。理论断裂角与预制非闭合裂纹类岩石脆性材料压剪断裂试验结果符合得较好。

钢桥面环氧沥青混凝土铺装层Ⅰ型裂缝的断裂判据

基于桥面铺装的裂缝特点及断裂力学理论,引入应力强度因子K和J积分对环氧沥青混凝土三点弯曲梁试验进行分析,研究了温度和初始缝高比对其断裂特性的影响。根据不同断裂特性,计算得到了环氧沥青混凝土断裂韧性KIC和J积分临界值JIC;并研究了初始缝高比对断裂参数的影响,建立了环氧沥青混凝土K-J双参数联合断裂判据。结果表明：环氧沥青混凝土在-15℃～5℃时发生脆性断裂;在5℃～25℃时发生弹塑性断裂;所建立的断裂判据可为桥面铺装的抗裂设计提供依据,并为铺装结构的裂缝修补时机研究提供参考。

数字图像相关法测定岩石Ⅰ-Ⅱ复合型裂纹应力强度因子

提出了一种通过数字图像相关方法测定岩石Ⅰ-Ⅱ复合型裂纹尖端位置和应力强度因子的试验方法。试验通过数字图像相关方法测定裂纹尖端区域位移场数据,将位移场数据带入极坐标系下位移场方程,计算裂纹尖端位置和应力强度因子。试验结果表明:采用该方法可以准确的测定岩石Ⅰ-Ⅱ复合型裂纹应力强度因子、裂纹尖端位置及裂纹扩展长度,解决了以往研究方法因不能准确测定裂纹尖端位置和扩展方向,而无法准确测定岩石应力强度因子的难题。

基于损伤理论的混凝土Ⅰ-Ⅱ复合型裂缝扩展角

基于混凝土断裂与损伤的基本理论,进行了Ⅰ-Ⅱ复合型裂缝扩展方向研究,研究结果表明:Ⅰ-Ⅱ复合型裂缝扩展趋势是随着缝端损伤场的变化而变化的。通过缝端损伤场及损伤梯度的计算,分析了Ⅰ-Ⅱ复合型裂缝从起裂至失稳断裂裂缝扩展方向的变化规律,得到了Ⅰ-Ⅱ复合型裂缝的起裂扩展角和失稳扩展角。将其与文献结果进行对比,对比结果表明:用损伤理论研究裂缝的扩展角是可行的。

Ⅰ-Ⅱ复合型裂缝应力强度因子和应变能释放率的关系

为了探究复合型裂缝的应力强度因子K和应变能释放率G的关系,基于最大应力准则,采用能量法对Ⅰ-Ⅱ复合型裂缝的扩展进行理论分析。根据单一型裂缝应力强度因子和应变能释放率的关系,推导出Ⅰ-Ⅱ复合型裂缝K与G的关系公式,利用Abaqus软件建立Ⅰ-Ⅱ复合型裂缝的有限元模型,计算Ⅰ-Ⅱ复合型裂缝的应力强度因子和应变能释放率,与推导公式的计算结果进行对比,二者误差仅为2.5%,验证了推导公式的合理性。